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Unformatted text preview: ECN 741: Public Economics Fall 2008 Diﬀerentiate w.r.t αand set α = 1 we get
k=1 Uik ck
k=1 Ujk ck
Uj Also, note that Ul = Wl , Uli = Wlg Gi and Ui = Wg Gi . Therefore,
Hi = − n
k=1 Uik ck Uil l
k=1 Uik ck Wlg l
Wg This can be generalized to utility functions of the form
u(c1 , . . . , ck , G(ck+1 , . . . , cn ), l)
in which, G(·) is homothetic. Then the result is that commodities (ck+1 , . . . , cn ) should be
taxed at uniform rate.
Exercise: Suppose consumer is endowed with y unit of good one that cannot be taxed
away. Does the uniform commodity taxation still hold? what if the utility function is
Exercise: Suppose government is restricted to setting taxed on c1 to zero. How would
modify the Ramsey problem? Does the uniform commodity taxation hold? 1.4 Intermediate good taxation Another powerful and important result in Ramsey taxation is that intermediate good shall
not be taxed.
Suppose there are two sectors. One sector produces commodity x1 that is consumed by
private agent, c1 and by government, g . Commodity x1 is produced using intermediate good
z and labor l1 as input according to the following production function f (x1 , z, l1 ) = 0.
The other sector, uses labor l2 as input to produce good x2 that can be used as input in
production of good x1 (that is z ) or it can be consumed (c2 and g2 ). The technology is the
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This note was uploaded on 12/10/2011 for the course MAT 121 taught by Professor Wong during the Fall '10 term at SUNY Stony Brook.
- Fall '10